Cheeger, Jeff; Yau, Shing-Tung A lower bound for the heat kernel. (English) Zbl 0481.35003 Commun. Pure Appl. Math. 34, 465-480 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 90 Documents MSC: 35A08 Fundamental solutions to PDEs 53C20 Global Riemannian geometry, including pinching 35K05 Heat equation 35B35 Stability in context of PDEs Keywords:n-dimensional Riemannian manifold; comparison; mean curvatures; Ricci curvatures PDF BibTeX XML Cite \textit{J. Cheeger} and \textit{S.-T. Yau}, Commun. Pure Appl. Math. 34, 465--480 (1981; Zbl 0481.35003) Full Text: DOI OpenURL References: [1] , and , Le Spectre d’une Variété Riemannienne, Lecture Notes in Math., No. 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971. [2] Manifolds All of Whose Geodesics are Closed, Erg. der Math. No. 93, Springer-Verlag, Berlin-Heidelberg-New York, 1978. [3] and , Geometry of Manifolds, Academic Press, New York, 1964. [4] Cheeger, Arch. Math. (Basel) 19 pp 558– (1968) · Zbl 0177.50201 [5] On the Hodge theory of Riemannian Pseudomanifolds, Proc. Symp. Pure Math., A.M.S., 1980, pp. 91–146. [6] Cheeger, J. Differential Geometry 6 pp 119– (1971) [7] and , On the diffraction of waves by conical singularities, preprint. · Zbl 0536.58032 [8] Cheng, Math. Z. 143 pp 289– (1975) [9] Debiard, Publ. RIMS, Kyoto Univ. 12 pp 391– (1976) [10] Gaffney, Annals of Math. 60 pp 140– (1945) [11] Gaffney, Ann. of Math. 60 pp 458– (1954) [12] and , Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Math, 699, Springer-Verlag, Berlin-Heidelberg-New York, 1979. · Zbl 0414.53043 [13] Michel, C. R. Acad. Sci. Paris, Ser. A 282 pp 1007– (1976) [14] and , Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. [15] Yau, Indiana Univ. Math. J. 25 pp 659– (1976) [16] Lectures on Semigroup Theory and Its Applications to Cauchy’s Problem in Partial Differential Equations, Tata Inst. of Fundamental Research, Bombay, 1957. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.